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sqrtinv.c
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Sun, Jul 13, 23:22

sqrtinv.c
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/*
% y = sqrtinv(q,vlab,K)
% SQRTINV Computes for PSD-cone, y = (Q / diag(sqrt(vlab)))', so that
% Y'*Y = inv(Q * diag(vlab) * Q').
%
% SEE ALSO sedumi
% ********** INTERNAL FUNCTION OF SEDUMI **********
function y = sqrtinv(q,vlab,K)
% This file is part of SeDuMi 1.1 by Imre Polik and Oleksandr Romanko
% Copyright (C) 2005 McMaster University, Hamilton, CANADA (since 1.1)
%
% Copyright (C) 2001 Jos F. Sturm (up to 1.05R5)
% Dept. Econometrics & O.R., Tilburg University, the Netherlands.
% Supported by the Netherlands Organization for Scientific Research (NWO).
%
% Affiliation SeDuMi 1.03 and 1.04Beta (2000):
% Dept. Quantitative Economics, Maastricht University, the Netherlands.
%
% Affiliations up to SeDuMi 1.02 (AUG1998):
% CRL, McMaster University, Canada.
% Supported by the Netherlands Organization for Scientific Research (NWO).
%
% This program is free software; you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation; either version 2 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program; if not, write to the Free Software
% Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
% 02110-1301, USA
*/
#include <math.h>
#include <string.h>
#include "mex.h"
#include "triuaux.h"
#include "blksdp.h"
#define Y_OUT plhs[0]
#define NPAROUT 1
#define Q_IN prhs[0]
#define V_IN prhs[1]
#define K_IN prhs[2]
#define NPARIN 3
/* ************************************************************
PROCEDURE qdivv - Computes Y = (Q / diag(sqrt(vlab)))'
************************************************************ */
void qdivv(double *y, const double *q,const double *v,const mwIndex n)
{
mwIndex i,j,jcol,inz;
double svi;
for(inz = 0, i = 0; i < n; i++){
svi = sqrt(v[i]);
for(j = 0, jcol = i; j < n; j++, jcol += n)
y[jcol] = q[inz++] / svi; /* y(i,j) = q(j,i) / svi */
}
}
/* complex case */
void prpiqdivv(double *y,double *ypi, const double *q,const double *qpi,
const double *v,const mwIndex n)
{
mwIndex i,j,jcol,inz;
double svi;
for(inz = 0, i = 0; i < n; i++){
svi = sqrt(v[i]);
for(j = 0, jcol = i; j < n; j++, jcol += n){
/* y(i,j) = conj(q(j,i)) / svi */
y[jcol] = q[inz] / svi;
ypi[jcol] = -qpi[inz] / svi; /* conjugate */
inz++;
}
}
}
/* ============================================================
MAIN: MEXFUNCTION
============================================================ */
/* ************************************************************
PROCEDURE mexFunction - Entry for Matlab
************************************************************ */
void mexFunction(const int nlhs, mxArray *plhs[],
const int nrhs, const mxArray *prhs[])
{
mwIndex i,k, nk, nksqr, lenud, lendiag, diagskip;
double *y;
const double *q,*v;
coneK cK;
/* ------------------------------------------------------------
Check for proper number of arguments
------------------------------------------------------------ */
mxAssert(nrhs >= NPARIN, "sqrtinv requires more input arguments.");
mxAssert(nlhs <= NPAROUT, "sqrtinv generates less output arguments.");
/* ------------------------------------------------------------
Disassemble cone K structure
------------------------------------------------------------ */
conepars(K_IN, &cK);
/* ------------------------------------------------------------
Get statistics of cone K structure
------------------------------------------------------------ */
lenud = cK.rDim + cK.hDim;
diagskip = cK.lpN + 2 * cK.lorN; /* diag for LP and Lorentz */
lendiag = diagskip + cK.rLen + cK.hLen;
/* ------------------------------------------------------------
Get inputs v, q
------------------------------------------------------------ */
mxAssert(mxGetM(V_IN) * mxGetN(V_IN) == lendiag, "v size mismatch");
mxAssert(mxGetM(Q_IN) * mxGetN(Q_IN) == lenud, "q size mismatch");
q = mxGetPr(Q_IN);
v = mxGetPr(V_IN) + diagskip; /* skip LP*/
/* ------------------------------------------------------------
Allocate output y
------------------------------------------------------------ */
Y_OUT = mxCreateDoubleMatrix(lenud, (mwSize)1, mxREAL);
y = mxGetPr(Y_OUT);
/* ------------------------------------------------------------
The actual job is done here:
------------------------------------------------------------ */
for(k = 0; k < cK.rsdpN; k++){ /* PSD: real symmetric */
nk = cK.sdpNL[k];
qdivv(y, q,v,nk);
nksqr = SQR(nk);
y += nksqr; q += nksqr; v += nk;
}
for(; k < cK.sdpN; k++){ /* complex Hermitian */
nk = cK.sdpNL[k];
nksqr = SQR(nk);
prpiqdivv(y,y+nksqr, q,q+nksqr, v, nk);
nksqr += nksqr;
y += nksqr; q += nksqr; v += nk;
}
}

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